Abstract
In this paper, the method of artificial boundary conditions for exterior quasilinear problems in concave angle domains is investigated. Based on the Kirchhoff transformation, the exact quasiliner elliptical arc artificial boundary condition is derived. Using the approximate elliptical arc artificial boundary condition, the finite element method is formulated in a bounded region. The error estimates are obtained. The effectiveness of our method is showed by some numerical experiments.
Highlights
IntroductionThe relation derived in (ii) and used in (iii) is called an artificial boundary condition, natural integral equation or DtN map
We propose an artificial boundary method using elliptical arc artificial boundary for exterior quasilinear problems in concave angle domains
We provide error estimates depend on the finite element mesh, the order of the artificial boundary condition and the location of artificial boundary
Summary
The relation derived in (ii) and used in (iii) is called an artificial boundary condition, natural integral equation or DtN map. Natural boundary reduction reduces the boundary value problem into a hypersingular integral equation on the artificial boundary It has many advantages, such as the positive-definite symmetry of stiffness matrices, the stability of approximate solutions, and can be coupled with the finite element method naturally and directly. The elliptical artificial boundary was generalised later for elongated domains mains problems [24]. We propose a new method of elliptical conditions tions forsolution the numerical solutionproblems of quasilinear problems in exterior elongated for the numerical of quasilinear in exterior elongated domains with domain concave angles.
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